11.1. Moments: Definition and Types

Try these first

1. 1.

   What is a raw moment?

   Hint

   Think about how we calculate averages.

2. 2.

   Write the formula for the mean.

   Hint

   It is the first moment.

3. 3.

   What is the formula for the first raw moment?

   • E[X^1]
   • E[X^2]
   • E[(X - μ)^1]

   Hint

   Consider the definition of raw moments.

4. 4.

   True or False: The first central moment is always equal to the mean.

   • True
   • False

   Hint

   Think about what a central moment measures.

5. 5.

   A discrete random variable X takes values 0 and 1 with probabilities 0.6 and 0.4 respectively. Calculate the mean and variance of X.

   Hint

   Use the formulas for mean and variance step by step.

6. 6.

   Given a continuous random variable with the pdf defined over a certain range, derive the first and second moments.

   Hint

   Remember to integrate over the proper limits.